How can I animate the visibility of a face?
You could use a Mask modifier if you really want to delete certain faces on a certain frame, however I'm not sure this is really what you want to do.
Mask modifier:
If you really want to delete a specific face (or faces) on a certain frame, then you can use the Mask modifier.

Select the faces you want to hide and assign them to a vertex group in Properties &gt; Object data &gt; Vertex groups

Add a mask modifier and select your vertex group and enable Invert by clicking the button next to the vertex group selector:


Keyframe the visibility of the modifier by hovering over the eye icon and pressing I.


If you want more variation, try using a reversed Build modifier. This will delete all faces in the object over time, either randomly or in order.
Fracturing:
If you are trying to make a more complex/realistic
You might also want to try the Cell fracture addon (see this post):

Or the explode modifier.